Given f(x)= x a^{2} -5; find:
f(x + h) - f(x)
You asked:
Evaluate the function \(f\left( x \right) = x {a}^{2} - 5\), \(f\left( x + h \right) - f\left( x \right)\).
MathBot Answer:
$$\begin{aligned}f\left( x + h \right) - f\left( x \right)&=a^{2} h\end{aligned}$$
$$\begin{aligned}f\left( x + h \right) - f\left( x \right)&=-\left(a^{2} x - 5\right) + a^{2} \left(h + x\right) - 5\\f\left( x + h \right) - f\left( x \right)&=- a^{2} x + 5 + a^{2} \left(h + x\right) - 5\\f\left( x + h \right) - f\left( x \right)&=- a^{2} x + 5 + a^{2} h + a^{2} x - 5\\f\left( x + h \right) - f\left( x \right)&=a^{2} h\\\end{aligned}$$