What is the inverse of f(x)=3(1/2 x-7)^2+8 ?

The inverse of f(x)=3(1/2 x-7)^2+8 is 2sqrt((x-8)/3)+14,-2sqrt((x-8)/3)+14

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inverse of f(x)=3(1/2 x-7)^2+8

inverse

f (x) = 3 (\frac{1}{2} x - 7)^{2} + 8

2 \frac{x - 8}{3} + 14, - 2 \frac{x - 8}{3} + 14

Solution steps

y = 3 (\frac{1}{2} x - 7)^{2} + 8

Replace

x

with

y

x = 3 (\frac{1}{2} y - 7)^{2} + 8

Solve for

y, x = 3 (\frac{1}{2} y - 7)^{2} + 8

2 \frac{x - 8}{3} + 14, - 2 \frac{x - 8}{3} + 14

2

5

f (x) = \frac{9}{2} x - 5

f (x) = - \frac{1}{5} x - \frac{3}{5}

What is the inverse of f(x)=3(1/2 x-7)^2+8 ?
The inverse of f(x)=3(1/2 x-7)^2+8 is 2sqrt((x-8)/3)+14,-2sqrt((x-8)/3)+14