What is (f o g)(36) if f(x)=6^x and g(x)=log6 x ?

We are given that f(x)= 6^x and g(x) = log(6) x We have to find fog(36) fog(36) = f(g(36)) => f(log(6) 36) => 6^(log (6) 36) we know that a^(log(a) x) = x => 36 The required solution for fog(36) = 36

According to the rule, (f o g)(x) = f(g(x)) So, (f o g)(36) = f(g(36)) We'll calculate g(36) = log6 (36) = log6 (6^2) = 2*log6 (6) = 2 (f o g)(36) = f(g(36)) = f(2) We'll substitute x by 2 in the expression of f(x): f(2) = 6^2 f(2) = 36 The result of composition of the functions is: (f o g)(36) = 36.

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What is (f o g)(36) if f(x)=6^x and g(x)=log6 x ?

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2 Answers

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on March 8, 2011 at 12:52 AM

We are given that f(x)= 6^x and g(x) = log(6) x

We have to find fog(36)

fog(36) = f(g(36))

=> f(log(6) 36)

=> 6^(log (6) 36)

we know that a^(log(a) x) = x

=> 36

The required solution for fog(36) = 36

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on March 8, 2011 at 12:51 AM

According to the rule, (f o g)(x) = f(g(x))

So, (f o g)(36) = f(g(36))

We'll calculate g(36) = log6 (36) = log6 (6^2) = 2*log6 (6) = 2

(f o g)(36) = f(g(36)) = f(2)

We'll substitute x by 2 in the expression of f(x):

f(2) = 6^2

f(2) = 36

The result of composition of the functions is: (f o g)(36) = 36.