Thread: I need help with functions.

1. I need help with functions.

1) Let f be the function defined by f(x) = 2x^4 + 5. Find f(a+h), f(2a-h).

2) Let f be the function defined by f(x) = -3x^2 – 3. Find f(1/2), f(-3/4).

3) Let f(x) = 3x – 4 and g(x) = (-1/3)x^2 – 4x. Find f+g, f-g, f/g, f∙g, f°g, g°f.

Thanks!!

2. 1) As $\displaystyle f(x)=2x^4+5$,

\displaystyle \begin{aligned} f(a+h)&=2(a+h)^4+5\\ &=2(a^4+4a^3h+6a^2h^2+4ah^3+h^4)+5. \end{aligned}

$\displaystyle f(a-h)$ can be found similarly.

2) If $\displaystyle f(x)=-3x^2-3$, then $\displaystyle f\left(\frac{1}{2}\right)$ and $\displaystyle f\left(-\frac{3}{4}\right)$ can be found by evaluating

$\displaystyle -3\left(\frac{1}{2}\right)^2-3$

and

$\displaystyle -3\left(-\frac{3}{4}\right)^2-3.$

3) If $\displaystyle f(x)=3x-4$ and $\displaystyle g(x)=-\frac{1}{3}x^2-4x$, then

\displaystyle \begin{aligned} (f+g)(x)&=(3x-4)+\left(-\frac{1}{3}x^2-4x\right)\\ (f-g)(x)&=(3x-4)-\left(-\frac{1}{3}x^2-4x\right)\\ (f/g)(x)&=\frac{3x-4}{\left(-\frac{1}{3}x^2-4x\right)}\\ (f\cdot g)(x)&=(3x-4)\cdot\left(-\frac{1}{3}x^2-4x\right)\\ \end{aligned}
\displaystyle \begin{aligned} (f\circ g)(x)&=\left(3\left(-\frac{1}{3}x^2-4x\right)-4\right).\\ \end{aligned}

Hope this helps.