Composition of Functions · Exercise 16

Determine the domain for each function in interval notation.

For the following exercise, find the indicated function given $f\left(x\right)=2x^2+1$ and $g\left(x\right)=3x-5.$

ⓐ $f\left(g\left(2\right)\right)$
ⓑ $f\left(g\left(x\right)\right)$
ⓒ $g\left(f\left(x\right)\right)$
ⓓ $\left(g\circ g\right)\left(x\right)$
ⓔ $\left(f\circ f\right)\left(-2\right)$

OpenStax, Algebra and Trigonometry 2e · §3.4 Composition of Functions · Exercise 16