Question

For the function f(x)=−4(2x​−3), evaluate f(8) by listing the steps in order.

a) -20
b) -12
c) -16
d) 0

What is the inverse function f−1(x) for f(x)=−4(2x​−3)?
a) f−1(x)=4x+12​
b) f−1(x)=−4x−12​
c) f−1(x)=−4x−8​
d) f−1(x)=4x+8​

Answer 1

f(x) = -4(2x - 3)

f(8) = -4(2(8) - 3)

= -4(16 - 3)

= -4(13)

= -52

None of those choices are correct.

`f(x) = - 4(2x - 3)`

`x = - 4(2 {f}^( - 1) (x) - 3)`

`2 {f}^( - 1) (x) - 3 = - (1)/(4) x`

`2 {f}^( - 1) (x) = - (1)/(4) x + 3`

`8 {f}^( - 1) (x) = - x + 12`

`{f}^( - 1) (x) = - (1)/(8) x + (3)/(2)`

None of those choices are correct.

Answer 2

To evaluate f(x) = -4(2x - 3) at x = 8, substitute 8 for x. The value of f(8) is -52. The inverse function f^(-1)(x) for f(x) = -4(2x - 3) is (x - 12) / -8.

Step-by-step explanation:

To evaluate the function f(x) = -4(2x - 3) at x = 8, we substitute 8 for x in the function.

f(8) = -4(2(8) - 3) = -4(16 - 3) = -4(13) = -52

So, f(8) = -52

The inverse function f^(-1)(x) for f(x) = -4(2x - 3) can be found by swapping x and y and solving for y.

To do this, we rewrite the function as x = -4(2y - 3) and solve for y.

x = -8y + 12

-8y = x - 12

y = (x - 12) / -8

So, f^(-1)(x) = (x - 12) / -8