Perform the operations of Functions:
1) Find \(f(g(x))\): \(f\left(x\right)=12x^{\frac{2}{3}}\) \(g\left(x\right)=8x^{\frac{5}{7}}\).
2) Let \(f\left(x\right)=27x^{\frac{4}{9}}\) and \(g\left(x\right)=x^{\frac{2}{3}}\). Find \(g\left(f\left(x\right)\right)\).
3) Let \(f\left(x\right)=14x+3\) and \(g\left(x\right)=x^2+3x-4.\) Find \(f\left(g\left(x\right)\right)\).
4) Let \(f\left(x\right)=14x+3\) and \(g\left(x\right)=x^2+3x-4.\) Find \(g\left(f\left(x\right)\right)\).
5) Let \(f\left(x\right)=14x+3\) and \(g\left(x\right)=x^2+3x-4.\) Find \(f\left(g\left(\frac{\sqrt{2}}{2}\right)\right)\).
6) Let \(f\left(x\right)=25x^{\frac{2}{3}}\) and \(g\left(x\right)=3x^{\frac{1}{4}}\), Find \(\left(f\cdot g\right)\left(x\right)\).
7) Let \(f\left(x\right)=7x^{\frac{4}{5}}\) and \(g\left(x\right)=-3x^{\frac{4}{5}},\) Find \(\left(f+g\right)\left(x\right)\) and \(\left(f-g\right)\left(x\right)\).
8) Let \( f(x)=\frac{1}{x}\) and \(g(x)=x^2-9 \), what is \( (f \circ g)(-3) \) and what is \( (g \circ f)(-3) \)?
Solution Bank
1) Find \(f(g(x))\): \(f\left(x\right)=12x^{\frac{2}{3}}\) \(g\left(x\right)=8x^{\frac{5}{7}}\).
2) Let \(f\left(x\right)=27x^{\frac{4}{9}}\) and \(g\left(x\right)=x^{\frac{2}{3}}\). Find \(g\left(f\left(x\right)\right)\).
3) Let \(f\left(x\right)=14x+3\) and \(g\left(x\right)=x^2+3x-4.\) Find \(f\left(g\left(x\right)\right)\).
4) Let \(f\left(x\right)=14x+3\) and \(g\left(x\right)=x^2+3x-4.\) Find \(g\left(f\left(x\right)\right)\).
5) Let \(f\left(x\right)=14x+3\) and \(g\left(x\right)=x^2+3x-4.\) Find \(f\left(g\left(\frac{\sqrt{2}}{2}\right)\right)\).
6) Let \(f\left(x\right)=25x^{\frac{2}{3}}\) and \(g\left(x\right)=3x^{\frac{1}{4}}\), Find \(\left(f\cdot g\right)\left(x\right)\).
7) Let \(f\left(x\right)=7x^{\frac{4}{5}}\) and \(g\left(x\right)=-3x^{\frac{4}{5}},\) Find \(\left(f+g\right)\left(x\right)\) and \(\left(f-g\right)\left(x\right)\).
8) Let \( f(x)=\frac{1}{x}\) and \(g(x)=x^2-9 \), what is \( (f \circ g)(-3) \) and what is \( (g \circ f)(-3) \)?
Solution Bank