Question

Please please help Given the function f(x)=1/3x*2-3x+5 determine the inverse relation

Answer 1

The inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

How to determine the inverse relation?

The function is given as

f(x)=1/3x^2-3x+5

Start by rewriting the function in vertex form

f(x) = 1/3(x - 9/2)^2 -7/4

Rewrite the function as

y = 1/3(x - 9/2)^2 -7/4

Swap x and y

x = 1/3(y - 9/2)^2 -7/4

Add 7/4 to both sides

x + 7/4= 1/3(y - 9/2)^2

Multiply by 3

3x + 21/4= (y - 9/2)^2

Take the square roots

y - 9/2 = √(3x + 21/4)

This gives

y = 9/2 + √(3x + 21/4)

Hence, the inverse relation of the function f(x)=1/3x*2-3x+5 is f-1(x) = 9/2 + √(3x + 21/4)

Read more about inverse functions at:

brainly.com/question/14391067

#SPJ1