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)
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