Maths · The composition of functions
Read the following information and answer the three items that follow: Let =\bol
Read the following information and answer the three items that follow: Let \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{x}^{2}+\boldsymbol{2} \boldsymbol{x}-\boldsymbol{5} \) and \( \boldsymbol{g}(\boldsymbol{x})= \) \( 5 x+30 \) What are the roots of the equation \( \boldsymbol{g}[\boldsymbol{f}(\boldsymbol{x})]=\mathbf{0} ? \)
- A. 1,-1
- B. -1,-1
- C. 1,1 \)
- D. 0,1
Step-by-step solution
First compute f(x)=x^2+2x-5. Then g(f(x))=5(x^2+2x-5)+30=5x^2+10x-25+30=5x^2+10x+5=5(x^2+2x+1)=5(x+1)^2. Set equal to 0: 5(x+1)^2=0 => (x+1)^2=0 => x=-1 (double root). Thus the roots are -1 and -1.
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