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

Find the domain of the function: $$f:x\rightarrow\sqrt[]{4-x^2}$$

Find the domain of the function: $$f:x\rightarrow\sqrt[]{x^2-4}$$

Find the inverse of the function $$f(x)=\frac{2-\sqrt[]{x}}{5}$$

If g(x)=2x+1 and h(x)=3x-2, what is the result of combining the functions hog(x)?

If $$f(x+2)=x^3-2x^2+x-7,$$ what is $$f(1).$$

If $$f(x-2)=x^3-2x^2+x-1,$$ what is $$f(1)$$ ?

Given that $$f(x)=2x^2-3$$ and $$g(x)=2x+1$$ where $$x\in R,$$ find gof(x).

Emma and Michael are playing a math game. They have two functions, f and g, defined on the set R of real numbers. Function f is defined as $$f:x\rightarrow12-\frac{x}{2},\ x\ne0$$ and function g is defined as $$g:x\rightarrow5x-1.$$ They want to find the value of gof(4). Can you help them?

Function h is defined on the set R of real numbers by $$h:x\rightarrow\frac{1}{\left(2x-1\right)},\ x\ne\frac{1}{2}.$$ Find $$h^{-1},$$ the inverse of h.

Given that $$f(x)=\frac{\left(x+1\right)}{2},$$ find $$f^{-1}(-2).$$

Given that $$f:\rightarrow\frac{(2x-1)}{(x+2)},$$ find $$f^{-1},$$ the inverse of f.

A function f(x) is defined on the set R, of real numbers, by $$f\left(x\right)=px^2+qx+2,$$ where p and q are constants. If f(-2)=0 and f(1)=3, find f(-4).

William, Anika, and Hannah are playing a math game. They have two functions, $$f\left(x\right)=\frac{2}{(1-x)}$$ and $$g\left(x\right)=\frac{\left(x-1\right)}{x}$$ . They want to find the inverse of the composition of these functions, $$(fog)^{-1}\left(\frac{1}{2}\right)$$ . Can you help them? Solve the problem and choose the correct option:

Given $$f\left(x\right)=\frac{2}{(1-x)}$$ and $$g\left(x\right)=\frac{\left(x-1\right)}{x},$$ where x is a real number; find $$g^{-1}of^{-1}\left(1\right).$$

Given that $$f(x)=\frac{(4x+5)}{(2x+1)}$$ and $$g(x)=3x+1,$$ where $$x\in R,$$ find the inverse of fog.