A value of each expression: a. (g \cdot f)(1). b. (f \cdot g)

iohanetc

iohanetc

Answered question

2021-09-11

A value of each expression:
a. (gf)(1).
b. (fg)(4)
c. (ff)(3)

Answer & Explanation

Laith Petty

Laith Petty

Skilled2021-09-12Added 103 answers

We can define composite functions as follows
(fg)(x)=f(g(x))
(gf)(x)=g(f(x))
Calculation:
a. Since (gf)(x)=g(f(x))
Substituting x=1 we get,
(gf)(1)=g(f(1))
(gf)(1)=g(2)
(gf)(1)=4
b. Since (fg)(x)=f(g(x))
Substituting x=4 we get,
(fg)(4)=f(g(4))
g(4) is not given in the table.
So (fg)(4) is not possible to calculate.
c. Since (ff)(x)=f(f(x))
Substituting x=3 we get,
(ff)(3)=f(f(3))
(ff)(3)=f(6)
(ff)(3)=7
Conclusion:
a. (gf)(1)=4
b. (fg)(4) is not possible to calculate.
c. (ff)(3)=7

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