How to find f(x) - PSAT Math

First find the value of f(100) = 0.1(100) + 7 = 10 + 7 = 17

Then find g(17) = 1000(17) + 4 = 17000 + 4 = 17004.

When we multiply a function by a constant, we multiply each value in the function by that constant. Thus, 2f(x) = 4x + 12. We then subtract g(x) from that function, making sure to distribute the negative sign throughout the function. Subtracting g(x) from 4x + 12 gives us 4x + 12 - (3x - 3) = 4x + 12 - 3x + 3 = x + 15. We then add 2 to x + 15, giving us our answer of x + 17.

Doing things in an orderly way is a friend to the test-taker.

g(3) = 5 f(3-2)

= 5 f(1)

= 5 \[ 12 + 6**∙**1 + 8\]

= 5 \[ 1 + 6 + 8\]

= 5 \[ 15\]

= 75

Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x2 – 12) + 7.

Distribute the 3: 3x2 – 36 + 7 = 3x2 – 29

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First, input the function of h into g. So f(x) = 4(.25πx + 5) – 3, then simplify this expression f(x) = πx + 20 – 3 (leave in terms of πsince our answers are in terms of π). Then plug in 1 for x to get π+ 17.

The one-time first-month cost is p, and the monthly cost is m, which gets multipled by every month but the first (of which there are n -1). The total cost is the first-month cost of p, plus the monthly cost for (i.e. times) n -1 months, which makes the total cost equal to p + m (n -1).

Explanation: Because of the square in the equation you know the greatest magnitude (absolute value) x value will give you the greatest solution. The greatest magnitude of X listed is -3. Alternatively you could multiple everything out (Solutions: A) 41, B) 17, C) -7, D) 17 E)20)

Explanation: The values of each answer are A)3 B) 2, C) 1, D)4, E)5.

Plug each value for x into the above equation and solve for f(x). f(1) provides the lowest value –5/3

To solve this problem, we look for an operation to perform on both sides that will leave n-2 by itself on one side. Dividing both sides by 25_n_-3 would leave n-2 by itself on the right side of the equqation, as shown below:

100n3p–1/25n–3 = 25n/25n–3

Remember that when dividing terms with the same base, we subtract the exponents, so the equation can be written as 100n0p–1/25 = n–2

Finally, we simplify to find 4_p–_1 = _n–_2.

Adding 12 to both sides and dividing by 4 yields (7y+12)/4.

By distribution we obtain **–**7x – 21 = – 7x + 20. This equation is never possibly true.

When functions are set up within other functions like in this problem, the function closest to the given variable is performed first. The value obtained from this function is then plugged in as the variable in the outside function. Since b(x) = –2x, and x = 2, the value we obtain from b(x) is –4. We then plug this value in for x in the a(x) function. So a(x) then becomes 2(–43) + (–4), which equals –132.

f(–3) = (–3)2 + 5 = 9 + 5 = 14

f(x) = 4x + 2

g(x) = 3x - 1

We have f(d) = 2g(d). We multiply each value in g(d) by 2.

4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)

4d + 2 = 6d - 2 (Add 2 to both sides.)

4d + 4 = 6d (Subtract 4d from both sides.)

4 = 2d (Divide both sides by 2.)

2 = d

We can plug that back in to double check.

4(2) + 2 = 6(2) - 2

8 + 2 = 12 - 2

10 = 10

Using the defined function, f(a) will produce the same result when substituted for x:

f(a) = _a_2 – 5

Setting this equal to 4, you can solve for a:

_a_2 – 5 = 4

_a_2 = 9

a = –3 or 3

Substitute -1 for in the given function.

If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that is 1, then you will have calculated 18.