Text Let f(x)=2x−3f(x)=2x-3f(x)=2x−3 and g(x)=x2+1g(x)=x^{2}+1g(x)=x2+1. (a) Write the expressions for (f∘g)(x)(f\circ g)(x)(f∘g)(x) and (g∘f)(x)(g\circ f)(x)(g∘f)(x). (b) Compute (f∘g)(2)(f\circ g)(2)(f∘g)(2) and (g∘f)(2)(g\circ f)(2)(g∘f)(2). Solution (a) Composing, (f∘g)(x)=f(g(x))=2(x2+1)−3=2x2−1,(f\circ g)(x)=f\big(g(x)\big)=2(x^{2}+1)-3=2x^{2}-1,(f∘g)(x)=f(g(x))=2(x2+1)−3=2x2−1, (g∘f)(x)=g(f(x))=(2x−3)2+1=4x2−12x+10.(g\circ f)(x)=g\big(f(x)\big)=(2x-3)^{2}+1=4x^{2}-12x+10.(g∘f)(x)=g(f(x))=(2x−3)2+1=4x2−12x+10. (b) Substituting x=2x=2x=2: (f∘g)(2)=2⋅4−1=7,(g∘f)(2)=4⋅4−24+10=2.(f\circ g)(2)=2\cdot 4-1=7,\qquad (g\circ f)(2)=4\cdot 4-24+10=2.(f∘g)(2)=2⋅4−1=7,(g∘f)(2)=4⋅4−24+10=2. (f∘g)(2)=7,(g∘f)(2)=2 \boxed{\,(f\circ g)(2)=7,\quad (g\circ f)(2)=2\,}(f∘g)(2)=7,(g∘f)(2)=2