Functions

Algebra Level 3

Given f(x) = 3x + 5 and fg(x) = 6x + 14 , find the value of g(2)


The answer is 7.

Viknes Selvam by Viknes Selvam , 23, Malaysia

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3 solutions

Nikhil Raj
Jun 4, 2017

f ( x ) = 3 x + 5................................................... ( g i v e n ) N o w , f ( g ( x ) ) = 6 x + 14 3 g ( x ) + 5 = 6 x + 14 3 g ( x ) = 6 x + 9 g ( x ) = 2 x + 3 ∴ g ( 2 ) = 7 f(x) = 3x + 5...................................................(given) \\ Now, f(g(x)) = 6x + 14 \\ 3g(x) + 5 = 6x + 14 \\ 3g(x) = 6x + 9 \\ g(x) = 2x + 3 \\ \therefore g(2) = \color{#D61F06}{\boxed{7}}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Say g(x)=y. so fg(x)=3y+5=6x+14.. 3y=6x+9.. y=2x+3.. g(x)=2x+3.. so, g(2)=7 ..

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How about this question if f(-3)=2 and f(-1)=-4 find f(7).

okijo setsu - 6 years, 10 months ago

Then the author of this problem should change f g ( x ) fg(x) to f ( g ( x ) ) f(g(x)) or ( f ∘ g ) ( x ) (f \circ g)(x) so as not to confuse with multiplication of functions.

Jaydee Lucero - 6 years, 9 months ago

inverse of f(x)=(x-5)/3.....so g(x0=f inverse of(6x+14). by substituting 6x+14 in inverse of f ..we get 2x+3.so g(2)=2*2+3

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