Question

1. ★ multiple choice what is $f(x) + g(x)$ if $f(x) = -7x^{2/3} - 1$ and $g(x) = 2x^{2/3} + 6$? \\(\boldsymbol{\text{\textbf{a}}}\\) $5x^{2/3} - 5$ \\(\boldsymbol{\text{\textbf{b}}}\\) $-5x^{2/3} + 5$ \\(\boldsymbol{\text{\textbf{c}}}\\) $9x^{2/3} + 7$ \\(\boldsymbol{\text{\textbf{d}}}\\) $-9x^{2/3} - 7$

Explanation:

Step1: Write the expression for \( f(x) + g(x) \)

We know that \( f(x) = -7x^{2/3} - 1 \) and \( g(x) = 2x^{2/3} + 6 \). So, \( f(x)+g(x)=(-7x^{2/3}-1)+(2x^{2/3}+6) \).

Step2: Combine like terms for \( x^{2/3} \) terms

For the \( x^{2/3} \) terms: \( -7x^{2/3}+2x^{2/3}=(-7 + 2)x^{2/3}=-5x^{2/3} \).

Step3: Combine the constant terms

For the constant terms: \( -1 + 6 = 5 \).

Step4: Write the final expression

Putting it together, \( f(x)+g(x)=-5x^{2/3}+5 \).

Answer:

B. \( -5x^{2/3} + 5 \)