Determine whether the function has an inverse function If it

Determine whether the function has an inverse function. If it does, find the inverse function. f(x) = Squareroot 8x + 6 a. f^1(x) = x^2 + 6/8 b. f^1(x) = -x^2 - 6/8 c. f^1 (x) = x^2 - 6/8 d. f^1(x) = x^2 + 6/8 e. No Inverse

Solution

f(x) = sqrt(8x +6)

Its a one-to -one function, if we draw a horizonatl line across the graph of f(x) it cuts the graph at one

spot only

To find inverse plug x=y and y=x , solve for y

y = sqrt( 8x +6)

x = sqrt(8y +6)

x^2 = 8y +6

y = (x^2 - 6)/8

f^-1(x) = ( x^2 - 6)/8

Option c