Question

Given the two functions f(x) and g(x), what is the smallest whole number value of x such that f (x) ≥ g(x). equations f(x) = 1/2 (2) g(x) = 5x + 2

Answer 1

Equate the functions for minimum value of x.

`\begin{gathered} f(x)=g(x) \\ (1)/(2)(2)^x=5x+2 \\ (2)^x=10x+4 \end{gathered}`

Check for x = 5,

`\begin{gathered} (2)^5=10\cdot5+4 \\ 32<54 \end{gathered}`

For x = 6,

`\begin{gathered} (2)^6=10\cdot6+4 \\ 64=64 \end{gathered}`

So for x = 6, the value of function f(x) and g(x) is equal and for values more than 6, the function f(x) is greater than function g(x).

Answe: x = 6