Question

Let f(x) = 6 x + 16. Find : f(x +h)-f(x) h = Simplify f(x +h)-f(x) h = Submit Question

Answer 1

`f(x)=\sqrt[]{6x+16}`

First, we need to solve for f(x + h). To do this, we only have to replace x with x + h, like this.

`\begin{gathered} f(x+h)=\sqrt[]{6(x+h)+16} \\ f(x+h)=\sqrt[]{6x+6h+16} \end{gathered}`

Now, we have a value for f(x) and f(x+h). Let's substitute this data to the equation being asked.

`(f(x+h)-f(x))/(h)=\frac{\sqrt[]{6x+6h+16}-\sqrt[]{6x+16}}{h}`

To simplify:

`\begin{gathered} (f(x+h)-f(x))/(h)=\frac{\sqrt[]{6x+6h+16}-\sqrt[]{6x+16}}{h} \\ (f(x+h)-f(x))/(h)=\frac{\sqrt[]{2(3x+3h+8)}-\sqrt[]{2(3x+8)}}{h} \\ (f(x+h)-f(x))/(h)=\frac{\sqrt[]{2}(\sqrt[]{3x+3h+8})-\sqrt[]{2}(\sqrt[]{3x+8})}{h} \\ (f(x+h)-f(x))/(h)=\frac{\sqrt[]{2}(\sqrt[]{3x+3h+8}-\sqrt[]{3x+8})}{h} \end{gathered}`

The simplified equation is the last equation above.