FUNCTIONS

Arjun, Evelyn, and Benjamin are three friends who love solving math problems. They came across a function $$g(x)=\frac{(5x-2)}{(3x+1)}/,\ x\ne-\frac{1}{3};$$ . They challenged each other to find the inverse of function g. Can you help them out?

Given that $$f:x\rightarrow2^x$$ and $$g:x\rightarrow3x-2,$$ find fg(2).

If $$f(x)=\frac{1}{(2-x)},\ x\ne2,$$ find $$f^{-1}(-\frac{1}{2}).$$

Two functions f and g are defined by $$f:x\rightarrow3x-1$$ and $$g:x\rightarrow2x^3,$$ evaluate $$fog\left(-2\right).$$

Two functions f and g are defined on the set, R, of real numbers by $$f:x\rightarrow2x-1$$ and $$g:x\rightarrow x^2+1.$$ find the value of $$f^{-1}og(3).$$

A function f(x) is defined on R, the set of real numbers by $$f:x\rightarrow\frac{\left(x+3)\right)}{(x-2)},(x\ne2).$$ Find $$f^{-1}(x).$$

Given that $$P=\left\{x:x\ is\ a\ prime\ factor\ of\ 6\right\}$$ is the domain of $$g(x)=x^2+3x-5,$$ find the range of g(x).

The inverse of a function is given by $$f^{-1}:x\rightarrow\frac{\left(x+1\right)}{4},$$ find f:x.

James, Sophia, and Liam are solving a math problem. They are trying to find the value of a function defined by $$f(x)=\frac{(3x+1)}{(x^2-1)}.$$ Can you help them? What is the value of $$f(-3)?$$

The function $$f:x\rightarrow\sqrt[]{4-2x},$$ is defined on the set of real numbers R. Find the domain of f:x