Question

Find and simplify.f(x)=7-x^2a) f(x+h)-f(x)b) f(x+h)-f(x)/h​

Answer 1

Answer:

a) $f(x+h)-f(x) = h(-h-2x)$

b)$\frac{ f(x+h)-f(x)}{h}=-h-2x$

Step-by-step explanation:

Our parent function is

$f(x)=7-x^2$

$f(x+h) = 7-(x+h)^2$

$= 7-(x^2+h^2+2xh)$

$=7-x^2-h^2-2xh$

$f(x+h)-f(x)= 7-x^2-h^2-2xh-(7-x^2)$

$= 7-x^2-h^2-2xh-7+x^2$

$f(x+h)-f(x) = -h^2-2xh$

taking out h as GCF

a) $f(x+h)-f(x) = h(-h-2x)$

also

b) $\frac{ f(x+h)-f(x)}{h}=\frac{h(-h-2x)}{h}$

$\frac{ f(x+h)-f(x)}{h}=-h-2x$