Question

If f(x)=2x^2+3x+1 and g(x)=x+5, what would f(g(x))

Answer 1

Answer: The answer is $2x^2+23x+66.$

Step-by-step explanation: The given functions are

$f(x)=2x^2+3x+1,\\\\g(x)=x+5.$

We are to find f(g(x)). To do this, first we need to evaluate g(x) and then we will apply the function f on the resulting function.

The evaluation is as follows:

$f(g(x))=f(x+5)=2(x+5)^2+3(x+5)+1=2(x^2+10x+25)+3x+15+1\\\\\Rightarrow f(g(x))=2x^2+23x+66.$

Thus, the correct answer is $2x^2+23x+66.$

Answer 2

Answer:

$\large\boxed{f(g(x))=2x^2+23x+66}$

Step-by-step explanation:

$f(x)=2x^2+3x+1\\g(x)=x+5\\\\f(g(x))=f(\underbrace{x+5}_{g(x)})\\\\\text{Instead of x put to the function f expression x + 5}:\\\\f(g(x))=2(x+5)^2+3(x+5)+1\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\ \text{and the distributive property}\\\\f(g(x))=2(x^2+2(x)(5)+5^2)+(3)(x)+(3)(5)+1\\\\f(g(x))=2(x^2+10x+25)+3x+15+1\\\\f(g(x))=(2)(x^2)+(2)(10x)+(2)(25)+3x+16\\\\f(g(x))=2x^2+20x+50+3x+16\\\\\text{combine like terms}\\\\f(g(x))=2x^2+(20x+3x)+(50+16)\\\\f(g(x))=2x^2+23x+66$