What is the inverse of f(x)=5[(x+3)/4-2]^2+6 ?

The inverse of f(x)=5[(x+3)/4-2]^2+6 is 4sqrt((x-6)/5)+5,-4sqrt((x-6)/5)+5

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inverse of f(x)=5[(x+3)/4-2]^2+6

inverse

f (x) = 5 [\frac{x + 3}{4} - 2]^{2} + 6

4 \frac{x - 6}{5} + 5, - 4 \frac{x - 6}{5} + 5

Solution steps

y = 5 [\frac{x + 3}{4} - 2]^{2} + 6

Replace

x

with

y

x = 5 [\frac{y + 3}{4} - 2]^{2} + 6

Solve for

y, x = 5 [\frac{y + 3}{4} - 2]^{2} + 6

4 \frac{x - 6}{5} + 5, - 4 \frac{x - 6}{5} + 5

(\frac{1}{2}, \frac{1}{3}), (\frac{3}{2}, \frac{5}{3})

f (x) = - 5 x^{2} + 6 x - 3

y = 2 x + 7, (4, - 8)

y = 3 x + 7

f (x) = \frac{x}{1 - x ^{2}}

What is the inverse of f(x)=5[(x+3)/4-2]^2+6 ?
The inverse of f(x)=5[(x+3)/4-2]^2+6 is 4sqrt((x-6)/5)+5,-4sqrt((x-6)/5)+5