Question

For f(x) = 5x + 2:

A) Find f(7)


B) Find f-1(x)


C) Find f-1(7)


D) Find f(f-1(7))

(i'm confused and no it's not multiple choice)

Answer 1

`A)\\f(x)=5x+2\\\\f(7):\ \text{Put x = 7 to the equation of the function:}\\\\f(7)=5(7)+2=35+2=37\\\\\boxed{f(7)=37}`

`B)\\f(x)=5x+2\to y=5x+2\\\\\text{exchange x to y}\\\\x=5y+2\\\\\text{solve for y}\\\\5y+2=x\qquad\text{subtract 2 from both sides}\\\\5y=x-2\qquad\text{divide both sides by 5}\\\\y=(1)/(5)x-(2)/(5)\\\\\boxed{f^(-1)(x)=(1)/(5)x-(2)/(5)}`

`C)\\f^(-1)(x)=(1)/(5)x-(2)/(5)\\\\f^(-1)(7):\ \text{Put x = 7 to the equation of the function}\ f^(-1)(x):\\\\f^(-1)(7)=(1)/(5)(7)-(2)/(5)=(7)/(5)-(2)/(5)=(7-2)/(5)=(5)/(5)=1\\\\\boxed{f^(-1)(7)=1}`

`D)\\f(f^(-1)(7))\\\\f^(-1)(7)=1,\ \text{Therefore put x = 1 to the equation of the function}\ f(x):\\\\f(1)=5(1)+2=5+2=7\\\\\boxed{f(f^(-1)(7))=7}`