fog(10) is the same as writing f(g(10)). Now we are given that f(x) = log x and g(x) = x^2.
To find fog(10)= f(g(10)), we first find g(10).
This is equal to 10^2.
Now substitute g(10) = 10^2 as the x value in f(x).
We get f(g(10)) = f( 10^2) = log (10^2)
Now we use the relation that log (a^b) = b* log a.
log (10^2) = 2 * log 10.
Now if the base of the log is 10 log 10= 1.
Else we can write the general result for fog(10) as 2 log 10.
f(x) = log x
g(x) = x^2
fog (10 ) = ?
First we need to determine fog (x):
We know that :
fog (x)= f (g(x)
Now we will substitute with g(x) value:
==> f(g(x) = f (x^2)
Now in f(x) we will substitute with x^2:
==> f(g(x) = log x^2
Now from logarithm properties we know that:
log a^b = b *log a
==> f(g(x)) = 2*log x
Now we will calculate fog (10)
==> fog (10 ) = f(g(10)) = 2*log 10
But log 10 = 1
==> fog (10) = 2*1 = 2
Then fog (10) = 2
Posted on
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