Answer
(a) $f(t,t^2)=2t$, (b) $f(x,x^2)=2x$, (c) $f(2y^2,4y)=2y(y+1)$
Work Step by Step
(a) Substitute $x=t$ and $y=t^2:$
$$f(t,t^2)=t+\sqrt[3]{t\cdot t^2}=t+\sqrt[3]{t^3}=t+t=2t$$
(b) Substitute $x=x$ and $y=x^2:$
$$f(x,x^2)=x+\sqrt[3]{x\cdot x^2}=x+\sqrt[3]{x^3}=x+x=2x$$
(c) Substitute $x=2y^2$ and $y=4y:$
$$f(2y^2,4y)=2y^2+\sqrt[3]{2y^2\cdot4y}=2y^2+\sqrt[3]{(2y)^3}=2y^2+2y=2y(y+1)$$
