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Answer:
[tex]f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}[/tex]
Step-by-step explanation:
We are given that
[tex]f(x)=tan(x)-\frac{2}{x}[/tex]
[tex]g(x)=x^2+8[/tex]
We have to find [tex]f(x)\times g(y)[/tex]
To find the value of [tex]f(x)\times g(y)[/tex] we will multiply f(x) by g(y)
[tex]g(y)=y^2+8[/tex]
Now,
[tex]f(x)\times g(y)=(tanx-\frac{2}{x})(y^2+8)[/tex]
[tex]f(x)\times g(y)=tan(x)(y^2+8)-\frac{2}{x}(y^2+8)[/tex]
[tex]f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}[/tex]
Hence,
[tex]f(x)\times g(y)=y^2tan(x)+8tan(x)-\frac{2y^2}{x}-\frac{16}{x}[/tex]