Relations and F...

Find the inverse of the linear function $$f$$.
$$f(x)=3x-2$$

Let $$f(x) = \begin{cases} 1+x, & 0\leq x\leq 2 \\ 3-x, & 2<x\leq 3 \end{cases}$$, then find $$(fof)(x)$$

$$f(x)\, =\, -1\, + |x\, -\, 2|, \, 0\, \leq\, x\, \leq\, 4$$
$$g(x)\, =\, 2\, -\, |x|,\, -1\, \leq\, x\, \leq\, 3$$
Which of the following is true

Let $$f$$ and $$g$$ be increasing and decreasing functions respectively from $$\displaystyle \left ( 0,\infty  \right )$$ to $$\left ( 0,\infty  \right )$$ and let $$h\left ( x \right )=f\left [ g\left ( x \right ) \right ]$$. If $$h\left ( 0 \right )=0$$ then $$ h\left ( x \right )-h\left ( 1 \right )$$ is

If f(x)=x+5 and g(x)=$$\displaystyle \sqrt{x^{2}-9}$$  then find the domain of gof(x)

Let $$f(x)=\ln x$$  and  $$g(x)\, =\, \left (\displaystyle \frac{x^{4}\, -\, x^{3}\, +\, 3x^{2}\, -\, 2x\, +\, 2}{2x^{2}\, -\, 2x\, +\, 3 )}\right )$$. The domain of $$f(g(x))$$ is

Find the inverse of the exponential function $$f$$.
$$f(x)={e}^{x-1}+3$$

If $$f(x) = x^{2} + x$$ and $$g(x) = \sqrt {x}$$, then the value of $$f(g(3))$$ is

Find the inverse of the logarithmic function $$f$$.
$$f(x)=\ln(x+2)-3$$