1. Iff is a real function defined by f(x) = x² + 7, find :f(t)-f(5)wh

1.	1. Iff is a real function defined by f(x) = x² + 7, find :f(t)-f(5)where t + 5
Answer» Given,f(x) = x^2 + 7 f(t) = t^2 + 7f(5) = 5^2 + 7 = 32 Therefore,f(t) - f(5)/t - 5= t^2 + 7 - 32/t - 5= t^2 - 25/t - 5= (t - 5)(t + 5)/t - 5= (t + 5) by definition f'(a)=f(x)-f(a)/x-a therefore we need the value of f'(a) f'(x)=2xf'(a)=2×5=10

1. Iff is a real function defined by f(x) = x² + 7, find :f(t)-f(5)where t + 5

Answer»

Given,f(x) = x^2 + 7

f(t) = t^2 + 7f(5) = 5^2 + 7 = 32

Therefore,f(t) - f(5)/t - 5= t^2 + 7 - 32/t - 5= t^2 - 25/t - 5= (t - 5)(t + 5)/t - 5= (t + 5)

by definition f'(a)=f(x)-f(a)/x-a

therefore we need the value of f'(a)

f'(x)=2xf'(a)=2×5=10