Advertisements
Advertisements
Question
If f(x) =` (2x−1)/ (5x−2) , x ≠ 2/5` Verify whether (fof) (x) = x
Solution
(fof) (x) = f(f(x))
= `"f" ((2x-1)/(5x-2))`
= `(2((2x-1)/(5x-2))-1)/(5((2x-1)/(5x-2))-2)`
= `(("4x" - 2 - 5"x" + 2)/(5"x" - 2))/((10"x" - 5 - 10"x" + 4)/(5"x" - 2))`
= `(4x-2-5x+2)/(10x-5-10x+4)`
= `(-x)/(-1)`
= x
APPEARS IN
RELATED QUESTIONS
If f(x) = x2, find `(f(1.1) - f(1))/((1.1 - 1))`
Let f : R+ → R, where R+ is the set of all positive real numbers, such that f(x) = loge x. Determine
(a) the image set of the domain of f
If f(x) = x2 − 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(iii) f g
If f(x) = sin [π2] x + sin [−π]2 x, where [x] denotes the greatest integer less than or equal to x, then
If f(m) = m2 − 3m + 1, find `f(1/2)`
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Let f be a subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a function from Z to Z? Justify?
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x3
Answer the following:
For any base show that log (1 + 2 + 3) = log 1 + log 2 + log 3
Answer the following:
If b2 = ac. prove that, log a + log c = 2 log b
Answer the following:
Show that, logy x3 . logz y4 . logx z5 = 60
Answer the following:
Find the range of the following function.
f(x) = `1/(1 + sqrt(x))`
Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`
If f(x) = `x^3 - 1/x^3`, then `f(x) + f(1/x)` is equal to ______.
Find the domain of the following functions given by f(x) = `(x^3 - x + 3)/(x^2 - 1)`
If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.
The expression \[\begin{array}{cc}\log_p\log_p\sqrt[p]{\sqrt[p]{\sqrt[p]{\text{...........}\sqrt[p]{p}}}}\\
\phantom{...........}\ce{\underset{n radical signs}{\underline{\uparrow\phantom{........}\uparrow}}}
\end{array}\]where p ≥ 2, p ∈ N; ∈ N when simplified is ______.
Let f be a function with domain [–3, 5] and let g(x) = | 3x + 4 |. Then, the domain of (fog) (x) is ______.
