Question

Given the following piecewise function, determine the value of g(4) - 3g(3).10%ifx<-3g(x) = {x+ + x2 + x^3* if x 2 3

Answer 1

Given the function

To find g(4) - 3g(3)

Step 1: Find g(4)

g(4) is obtained by substituting 4 into the piecewise function for a range of x greater than or equal to 3

`\begin{gathered} \sin ce\text{ 4 }\ge3 \\ \text{then} \\ g(x)=x^4+x^2+x-3 \\ g(4)=4^4+4^2+4-3 \\ g(4)=256+16+4-3 \\ g(4)=273 \end{gathered}`

Step 2: find 3g(3)

we will first find g(3)

g(3) is obtained by substituting 3 into the piecewise function for a range of x greater than or equal to 3

`\begin{gathered} \sin ce\text{ 3}\ge3 \\ \text{then} \\ g(x)=x^4+x^2+x-3 \\ g(3)=3^4+3^2+3-3 \\ g(3)=90 \end{gathered}`

We can now find 3g(3)

`\begin{gathered} 3g(3)\text{ } \\ \text{simply means} \\ 3\text{ x g(3)} \\ where\text{ g(3)=90} \\ 3g(3)=3\text{ x 90 =270} \end{gathered}`

Step 3: Find g(4) - 3g(3)

`\begin{gathered} g\mleft(4\mright)-3g\mleft(3\mright)=273-270 \\ g\mleft(4\mright)-3g\mleft(3\mright)=3 \end{gathered}`

Answer = 3