Question

Select the correct answer. Find the Inverse of function A F(x)=1/3 -1/2x

Answer 1

Answer:

If you actually meant f(x)=2x+3x−1 ,

then note it can be rewritten as:

f(x)=2x−2+5x−1=2+5x−1=y

At this point you can find x in terms of y (“make x the subject”):

y−2=5x−1⟹1y−2=x−15

⟹x=5y−2+1=y+3y−2

Switch variables back to x, and you have the inverse function of f:

g(x)=x+3x−2

How do you know you’ve calculated correctly? The composition of f with g should result in x — that is, evaluate f(g) and you should get the result x: