Examples

Solve the Function Operation
f(x)=3x+5 , g(x)=x3 , (gf)
Step 1
Set up the composite result function.
g(f(x))
Step 2
Evaluate g(3x+5) by substituting in the value of f into g.
g(3x+5)=(3x+5)3
Step 3
Use the Binomial Theorem.
g(3x+5)=(3x)3+3(3x)25+3(3x)52+53
Step 4
Simplify each term.
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Step 4.1
Apply the product rule to 3x.
g(3x+5)=33x3+3(3x)25+3(3x)52+53
Step 4.2
Raise 3 to the power of 3.
g(3x+5)=27x3+3(3x)25+3(3x)52+53
Step 4.3
Apply the product rule to 3x.
g(3x+5)=27x3+3(32x2)5+3(3x)52+53
Step 4.4
Multiply 3 by 32 by adding the exponents.
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Step 4.4.1
Move 32.
g(3x+5)=27x3+32(3x2)5+3(3x)52+53
Step 4.4.2
Multiply 32 by 3.
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Step 4.4.2.1
Raise 3 to the power of 1.
g(3x+5)=27x3+32(3x2)5+3(3x)52+53
Step 4.4.2.2
Use the power rule aman=am+n to combine exponents.
g(3x+5)=27x3+32+1x25+3(3x)52+53
g(3x+5)=27x3+32+1x25+3(3x)52+53
Step 4.4.3
Add 2 and 1.
g(3x+5)=27x3+33x25+3(3x)52+53
g(3x+5)=27x3+33x25+3(3x)52+53
Step 4.5
Raise 3 to the power of 3.
g(3x+5)=27x3+27x25+3(3x)52+53
Step 4.6
Multiply 5 by 27.
g(3x+5)=27x3+135x2+3(3x)52+53
Step 4.7
Multiply 3 by 3.
g(3x+5)=27x3+135x2+9x52+53
Step 4.8
Raise 5 to the power of 2.
g(3x+5)=27x3+135x2+9x25+53
Step 4.9
Multiply 25 by 9.
g(3x+5)=27x3+135x2+225x+53
Step 4.10
Raise 5 to the power of 3.
g(3x+5)=27x3+135x2+225x+125
g(3x+5)=27x3+135x2+225x+125
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 [x2  12  π  xdx ] 
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