Given, f: R → R and g: R → R
So, gof: R → R and fog: R → R
f(x) = 8x3 and g(x) = \( x^{\dfrac{1}{3}}\)
(gof) (x) = g (f (x))
= g (8x3)
= \(( 8x^3) x^{\dfrac{1}{3}}\)
= \( ( 2x^3) x^{\dfrac{1}{3}}\)
= 2x
Now, (fog) (x) = f (g (x))
= \(f( x^{\dfrac{1}{3}})\)
= \( 8( x^{\dfrac{1}{3}})^3\)
= 8x
Answered by Aaryan | 1 year agoLet A be the set of first five natural and let R be a relation on A defined as follows: (x, y) R x ≤ y
Express R and R-1 as sets of ordered pairs. Determine also
(i) the domain of R‑1
(ii) The Range of R.
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If f: R → R be defined by f(x) = x3 −3, then prove that f−1 exists and find a formula for f−1. Hence, find f−1 (24) and f−1 (5).
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