Question

★ FUNCTIONS ★

If f(x) = 9 x+ 5 is a relation from R to R then find f^-1 and find f ^-1( 3)

PLEASE EXPLAIN EVERYTHING REGARDING YOUR INTERPRETATION

Answer 1

Given,

f ( x) = 9x + 5

To find inverse function, let's see if it's a bijective function.

It is a bijective function as it is a linear function.

Taking f ( x) = y as the range of bijective function is co - domain.

y = 9x + 5

y -5 = 9x

y -5 /9 = x

x = y -5 /9

We know that, f(x)= y then x = f^-1(y)

f^-1(y)= y -5/9

Replacing by x

f^-1(x) = x-5/9

Now, f^-1 = { x,x-5/9 }

And

f^-1(3)=3-5/9 = -2/9

Hope helped! ^^