Question

Help please quick will be given enough points

Answer 1

A)

`\\\\\text{Given that,} ~ g(x) = \frac 13 x + 5 \\\\\text{Write g(x) as}~ y = \frac 13 x +5 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~x = \frac 13y +5 \\\\\implies 3x = y + 15~~~~~~~~~~~~~~~~~~~;[\text{Multiply both sides by 3]}\\\\\implies y = 3x -15\\\\\implies g^(-1) (x) = 3x -15 \\`

B)

`\left(g \circ} g^(-1) \right)(x)\\\\=g\left(g^(-1)(x) \right)\\\\=g(3x-15)\\\\=\frac 13\cdot(3x-15)+5\\\\=x -5 +5\\\\=x`