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lesya692 [45]
3 years ago
13

If f(x) = 6x – 4, then f^-1(x)=

Mathematics
1 answer:
guapka [62]3 years ago
8 0

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) withy 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

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