Question

evaluate the function for the given value of x.

1. ( g(x) = x^5 + 3x^2 - 2x - 9 ); ( x = 2 )

1. ( f(x) = 2sqrt3{x + 7} ); ( x = -1 ) (go ahead and report your answer as a decimal)

Explanation:

Problem 4:

Step 1: Substitute \( x = 2 \) into \( g(x) \)

We have \( g(x)=x^{5}+3x^{2}-2x - 9 \), so substitute \( x = 2 \) into each term:
\( x^{5}=2^{5}=32 \), \( 3x^{2}=3\times(2)^{2}=3\times4 = 12 \), \( - 2x=-2\times2=-4 \)

Step 2: Calculate the value

Now, sum up the terms: \( g(2)=32 + 12-4 - 9 \)
First, \( 32+12 = 44 \), then \( 44-4=40 \), and \( 40 - 9=31 \)

Step 1: Substitute \( x=-1 \) into \( f(x) \)

We have \( f(x)=2\sqrt[3]{x + 7} \), substitute \( x=-1 \) into the cube - root:
\( x + 7=-1 + 7=6 \)

Step 2: Calculate the cube - root and multiply by 2

First, find \( \sqrt[3]{6}\approx1.817 \) (using a calculator to find the cube - root of 6). Then multiply by 2: \( f(-1)=2\times1.817 = 3.634 \)

Answer:

\( 31 \)

Problem 5: