Question

question 7
let $f(x) = 2x + 3$ and $g(x) = 5x + 7$. write a formula for each of the following functions and then simplify.

a. $f + g = $

b. $f - g = $

c. $g - f = $

d. $g + f = $

e. $fg = $

f. $ff = $

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Explanation:

Step1: Define given functions

$f(x)=2x+3$, $g(x)=5x+7$

Step2: Compute $f+g$ (sum)

$f(x)+g(x)=(2x+3)+(5x+7)=7x+10$

Step3: Compute $f-g$ (difference)

$f(x)-g(x)=(2x+3)-(5x+7)=-3x-4$

Step4: Compute $g-f$ (reverse difference)

$g(x)-f(x)=(5x+7)-(2x+3)=3x+4$

Step5: Compute $g+f$ (commutative sum)

$g(x)+f(x)=(5x+7)+(2x+3)=7x+10$

Step6: Compute $fg$ (product)

$f(x)g(x)=(2x+3)(5x+7)=10x^2+14x+15x+21=10x^2+29x+21$

Step7: Compute $ff$ (square of $f$)

$f(x)f(x)=(2x+3)^2=4x^2+12x+9$

Answer:

a. $7x+10$
b. $-3x-4$
c. $3x+4$
d. $7x+10$
e. $10x^2+29x+21$
f. $4x^2+12x+9$