Janu16 one year ago Let f(x) = 3x^2 – x + 2 and g(x) = 5x^2 – 1. Find f(g(x)). Show each step of your work.

1. Janu16

@peachpi

2. IrishBoy123

$$g(x) = 5x^2 – 1$$ $$f(x) = 3x^2 – x + 2$$ $$f[g(x)] = f(5x^2 – 1) = 3[5x^2 – 1]^2 – [5x^2 – 1] + 2$$ this what you meant?? hope it helps :p

3. anonymous

$$\bf f(x)=3x^2-x+2\qquad g(x)={\color{brown}{ 5x^2-1 }} \\ \quad \\ f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ g(x)}})^2-({\color{brown}{ g(x)}})+2 \\ \quad \\ f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ 5x^2-1}})^2-({\color{brown}{ 5x^2-1}})+2$$

4. Janu16

so do you sole this?

5. anonymous

just distribute and simplify, sure

6. Janu16

25x^2-3x^2+25x^2-3^2+2?

7. anonymous

hmm, notice, the 1st term has an squared binomial you need to expand that one first

8. anonymous

$$\bf f(\ {\color{brown}{ g(x)}}\ )=3x({\color{brown}{ 5x^2-1}})^2-({\color{brown}{ 5x^2-1}})+2 \\ \quad \\ f(g(x))=3x({\color{brown}{ 25x^4-10x^2+1}})-5x^2+1+2$$

9. Janu16

why x4

10. Janu16

@jdoe0001

11. anonymous

$$\bf (5x^2-1)^2\iff (5x^2-1)(5x^2-1)\implies (25x^4-10x^2+1)$$

12. anonymous

you can FOIL if you want

13. Janu16

ojok