Solve the Function Operation

Problem

ƒ(g(x−1))* where *ƒ(x)=x2,g(x)=2*x+5,h(x)=x2−1

Solution

1. Evaluate the inner expression g*(x−1) by substituting x−1 into the function g(x)=2*x+5

g*(x−1)=2*(x−1)+5

2. Simplify the expression for g*(x−1) by distributing the constant and combining like terms.

g*(x−1)=2*x−2+5

g*(x−1)=2*x+3

3. Substitute the result 2*x+3 into the function ƒ(x)=x2 to find ƒ*(g*(x−1))

ƒ*(g*(x−1))=(2*x+3)2

4. Expand the squared binomial using the formula (a+b)2=a2+2*a*b+b2

ƒ*(g*(x−1))=(2*x)2+2*(2*x)*(3)+3

ƒ*(g*(x−1))=4*x2+12*x+9

Final Answer

ƒ*(g*(x−1))=4*x2+12*x+9

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