Question

If $f\left(x\right)=x^2$ and $g\left(x\right)=2x-6$, find the following functions:
$(f+g)\left(x\right),(f\times g)\left(x\right),(f\circ g)\left(x\right),(f\circ f)\left(x\right),g^{-1}\left(x\right)$

Answer 1

• Given $f\left(x\right)=x^2$ and $g\left(x\right)=2x-6$
• $(f+g)\left(x\right)=f\left(x\right)+g\left(x\right)=x^2+2x-6$
• $(f\times g)\left(x\right)=f\left(x\right)\times g\left(x\right)=x^2(2x-6)=2x^3-6x^2$
• $\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right)=f(2x-6)={(2x-6)}^2$
• $\left(fof\right)\left(x\right)=f\left(f\right(x\left)\right)=f\left(x^2\right)=x^4$
• $g^{-1}\left(x\right)=(x+6)/2$