Find f(g(x)) f(x)=x^2-5x-10 , g(x)=-7x+14

Problem

ƒ(g(x)),ƒ(x)=x2−5*x−10,g(x)=−7*x+14

Solution

1. Identify the outer function ƒ(x) and the inner function g(x)

2. Substitute the expression for g(x) into every instance of x in the function ƒ(x)

ƒ*(g(x))=(−7*x+14)2−5*(−7*x+14)−10

3. Expand the squared binomial (−7*x+14)2 using the formula (a+b)2=a2+2*a*b+b2

(−7*x+14)2=49*x2−196*x+196

4. Distribute the constant −5 into the terms of the second part of the expression.

−5*(−7*x+14)=35*x−70

5. Combine all parts of the expression together.

ƒ*(g(x))=49*x2−196*x+196+35*x−70−10

6. Simplify the expression by combining like terms.

ƒ*(g(x))=49*x2−161*x+116

Final Answer

ƒ*(g(x))=49*x2−161*x+116

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