If the functions f x and g x are defined by f x -5 x -2 - g x - x -2-3 then find the value of gf 3-A- 5B-C- 11-3D- 17

The correct option is A 5Given, f(x) = 5x + 2 and g(x) = x 2/3 ∵ gf(x) = g[f(x)] ∴ nbsp;gf(3) = g[f(3)] nbsp; nbsp; nbsp; nbsp; nbsp; nbs ...

You visited us 9 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Composition of Function

If the functi...

Question

If the functions $f (x) and g (x)$ are defined by $f (x) = 5 x + 2; g (x) = \frac{x - 2}{3}$ then find the value of $g f (3) .$

\frac{11}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 5
$Given, f (x) = 5 x + 2 and g (x) = \frac{x - 2}{3}$
$∵ g f (x) = g [f (x)]$
$∴ g f (3) = g [f (3)]$
$= g [5 (3) + 2] = g [17] = \frac{17 - 2}{3} = \frac{15}{3} = 5$

$∴ g f (3) = 5$

Suggest Corrections

Similar questions

Q. If the functions

f (x) and g (x)

are defined by

f (x) = 5 x + 2; g (x) = \frac{x - 2}{3}

then find the value of

g o f (3) .

Q. Assertion(A):

f (x) = log (x - 2) + log (x - 3)

and

g (x) = log (x - 2) (x - 3)

then

f (x) = g (x)

Reason (R): Two functions

f (x)

and

g (x)

are said to be equal if they are defined on the same domain

A

and the co-domain

B

f (x) = g (x) \forall x \in A

If $f (x)$ and $g (x)$ are real function defined by
$f (x) = {\begin{matrix} x, x i s r a t i o n a l 0, x i s i r r a t i o n a l \end{matrix}$ and $g (x) = {\begin{matrix} 0, x i s r a t i o n a l x, x i s i r r a t i o n a l \end{matrix}$ ,
then $(f - g) (x)$ is

Q. Two functions

f (x)

and

g (x)

are defined as

f (x) = {log}_{10} ∣ ∣ ∣ \frac{x - 2}{x^{2} - 10 x + 24} ∣ ∣ ∣

and

g (x) = {sin}^{- 1} (\frac{2 [x] - 3}{15})

, where [.] denotes greatest integer function, then the number of even integers for which

f (x) + g (x)

is defined, is

Q. Let two functions are defined as

g (x) = {\begin{matrix} x^{2}, & - 1 \leq x \leq 2 x + 2, & 2 \leq x \leq 3 \end{matrix},

and

f (x) = {\begin{matrix} x + 1 & x \leq 1 2 x + 1 & 1 < x \leq 2, \end{matrix}

then find

g o f

(1)

Join BYJU'S Learning Program

If the functions f(x) and g(x) are defined by f(x)=5x+2; g(x)=x−23 then find the value of gf(3).

The correct option is C 5Given, f(x)=5x+2 and g(x)=x−23 ∵gf(x)=g[f(x)] ∴gf(3)=g[f(3)] =g[5(3)+2]=g[17]=17−23=153=5 ∴gf(3)=5

If the functions $f (x) and g (x)$ are defined by $f (x) = 5 x + 2; g (x) = \frac{x - 2}{3}$ then find the value of $g f (3) .$

The correct option is C 5
$Given, f (x) = 5 x + 2 and g (x) = \frac{x - 2}{3}$
$∵ g f (x) = g [f (x)]$
$∴ g f (3) = g [f (3)]$
$= g [5 (3) + 2] = g [17] = \frac{17 - 2}{3} = \frac{15}{3} = 5$

$∴ g f (3) = 5$