Relations and F...

If $$f(x)=\displaystyle\frac{1}{3}x+3$$, then find $$f^{-1}(x)$$.

If $$f(x)=2x^3$$ and $$g(x)=3x$$, calculate the value of $$g(f(-2))-f(g(2))$$.

Find the inverse of the quadratic function $$f$$.
$$f(x)=-{x}^{2}+2, x>=0$$

Find the inverse of the cube root function $$f$$.
$$f(x)={(x+1)}^{1/3}$$

Find the inverse of the logarithmic function $$f$$.
$$f(x)=\ln(x)$$

Find the inverse of the square root function $$f$$.
$$f(x)=\sqrt{x-1}$$

Given two functions $$f(x)$$ and $$g(x)$$ such that $$f(x) = \sin (arctan x), g(x) =\tan (arc\sin x)$$, and $$0\leq x < \dfrac {\pi}{2}$$. The value of the composite function $$f\left (g\left (\dfrac {\pi}{10}\right )\right ) $$ is:

If $$f(x) = 1 - 4x$$, and $$f^{-1}(x)$$ is the inverse of $$f(x)$$, then the value of  $$f(-3) f{-1}(-3)=$$ is:

Given that $$f(x) = \dfrac {2x}{5} + \dfrac {7}{3}$$, find $$ f^{-1} (x) $$.