Answer:
a) [tex]f(x+h)-f(x) = h(-h-2x) [/tex]
b)[tex] \frac{ f(x+h)-f(x)}{h}=-h-2x[/tex]
Step-by-step explanation:
Our parent function is
[tex]f(x)=7-x^2[/tex]
[tex]f(x+h) = 7-(x+h)^2[/tex]
[tex]= 7-(x^2+h^2+2xh) [/tex]
[tex]=7-x^2-h^2-2xh[/tex]
[tex]f(x+h)-f(x)= 7-x^2-h^2-2xh-(7-x^2) [/tex]
[tex]= 7-x^2-h^2-2xh-7+x^2[/tex]
[tex]f(x+h)-f(x) = -h^2-2xh[/tex]
taking out h as GCF
a) [tex]f(x+h)-f(x) = h(-h-2x) [/tex]
also
b) [tex]\frac{ f(x+h)-f(x)}{h}=\frac{h(-h-2x)}{h}[/tex]
[tex] \frac{ f(x+h)-f(x)}{h}=-h-2x[/tex]
