Question

Find f inverse of x, the inverse of the function f of x equals 4 x plus 6.



Drag numbers into the blanks to complete the expression for f inverse of x.

Response area with 2 blank spaces
f inverse of x equals
Blank space 1 empty
x plus
Blank space 2 empty
Answer options with 8 options.

Answer 1

To find the inverse of the function \( f(x) = 4x + 6 \), we will follow these steps:

1. Replace \( f(x) \) with \( y \):
\[
y = 4x + 6
\]

2. Swap \( x \) and \( y \) to find the inverse:
\[
x = 4y + 6
\]

3. Solve for \( y \):
\[
x - 6 = 4y
\]
\[
y = \frac{x - 6}{4}
\]

Thus, the inverse function can be expressed as:
\[
f^{-1}(x) = \frac{1}{4}(x - 6)
\]

Rewriting it to fit the format requested:
\[
f^{-1}(x) = \frac{1}{4}x - \frac{6}{4}
\]

This simplifies to:
\[
f^{-1}(x) = \frac{1}{4}x - \frac{3}{2}
\]

Now we can fill in the blanks:

- Blank space 1: \( \frac{1}{4} \)
- Blank space 2: \( -\frac{3}{2} \)

So, the completed expression is:
\[
f^{-1}(x) = \frac{1}{4}x - \frac{3}{2}
\]