Solve the Function Operation f(x)=5x^2-2x , g(x)=8x+3 , f(g(k))

Problem

ƒ(x)=5*x^2−2*x,g(x)=8*x+3,ƒ*(g(k))

Solution

1. Identify the inner function g(k) by substituting k into the expression for g(x)

g(k)=8*k+3

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

ƒ*(g(k))=5*(8*k+3)^2−2*(8*k+3)

3. Expand the squared binomial (8*k+3)^2 using the identity (a+b)^2=a^2+2*a*b+b^2

(8*k+3)^2=64*k^2+48*k+9

4. Distribute the constants 5 and −2 into their respective parentheses.

ƒ*(g(k))=5*(64*k^2+48*k+9)−16*k−6

ƒ*(g(k))=320*k^2+240*k+45−16*k−6

5. Combine like terms to find the final simplified expression.

ƒ*(g(k))=320*k^2+224*k+39

Final Answer

ƒ*(g(k))=320*k^2+224*k+39

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