Which function is the inverse of the function f? $$ f(x)=4 x-5 $$ A. $$ j(x)=\frac{1}{4} x-\frac{1}{5} $$ B. $$ g(x)=\frac{1}{4} x+\frac{5}{4} $$ C. $$ k(x)=-4 x+5 $$ D. $$ h(x)=5 x-4 $$

Question

UpStudy AI · Accepted Answer

To find the inverse of the function $$ f(x) = 4x - 5 $$, follow these steps:

1. **Start with the original function:**
   $$
   y = 4x - 5
   $$

2. **Solve for $$ x $$ in terms of $$ y $$:**
   $$
   y + 5 = 4x \
   x = \frac{y + 5}{4} \
   x = \frac{1}{4}y + \frac{5}{4}
   $$

3. **Express the inverse function $$ f^{-1}(x) $$:**
   $$
   f^{-1}(x) = \frac{1}{4}x + \frac{5}{4}
   $$

Comparing this with the given options:

- **A.** $$ j(x) = \frac{1}{4}x - \frac{1}{5} $$ ❌
- **B.** $$ g(x) = \frac{1}{4}x + \frac{5}{4} $$ ✔️
- **C.** $$ k(x) = -4x + 5 $$ ❌
- **D.** $$ h(x) = 5x - 4 $$ ❌

**Answer:** B. $$ g(x)=\frac{1}{4} x+\frac{5}{4} $$
The inverse function is $$ g(x) = \frac{1}{4}x + \frac{5}{4} $$.

Which function is the inverse of the function f?

A.
B.
C.
D.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions

Which function is the inverse of the function f? A. B. C. D.