Question

If f:N→N, g:N→N and h:N→R is defined f(x)=3x-5, g(y)=6y^2 and h(z)=tan⁡z, find ho(gof).

(a) tan⁡(6(3x-5))

(b) tan⁡(6(3x-5)^2)

(c) tan⁡(3x-5)

(d) 6 tan⁡(3x-5)^2

I had been asked this question by my school teacher while I was bunking the class.

The query is from Composition of Functions and Invertible Function in division Relations and Functions of Mathematics – Class 12

Answer 1

The correct answer is (b) tan⁡(6(3x-5)^2)

The best I can explain: Given that, f(x)=3x-5, g(y)=6y^2 and h(z)=tan⁡z,

Then, ho(gof)=hο(g(f(x))=h(6(3x-5)^2)=tan⁡(6(3x-5)^2)

∴ ho(gof)=tan⁡(6(3x-5)^2)