Question

If f(x) = 6x – 4, then f^-1(x)=

Answer 1

Answer:

$f^{-1}(x)=\frac{x}{6}+\frac{2}{3}$

Step-by-step explanation:

Given function.

$f(x)=6x-4$

To find the inverse function $f^{-1}(x)$

Step 1:

Replace $f(x)$ with$y$ in the function.

$y=6x-4$

Step 2:

Interchange $y$ with $x$ in the equation.

$x=6y-4$

Step 3:

Solve for $y$.

We have $x=6y-4$

Adding 4 to both sides,

$x+4=6y-4+4$

$x+4=6y$

Dividing each term by 6 to isolate $y$

$\frac{x}{6}+\frac{4}{6}=\frac{6y}{6}$

$\frac{x}{6}+\frac{4}{6}=y$

Simplifying fractions by dividing the numerator and denominator by  their GCF.

$\frac{x}{6}+\frac{4\div 2}{6\div 2}=y$

$\frac{x}{6}+\frac{2}{3}=y$

Thus the equation of $y$ is:

$y=\frac{x}{6}+\frac{2}{3}$

Step 4:

Replace $y$ with $f^{-1}(x)$

$f^{-1}(x)=\frac{x}{6}+\frac{2}{3}$ (Answer)

Thus, we have the inverse function