Verify if f(x) and g(x) are inverse to each other in each case.
Problem 1 :
f(x) = x + 3
g(x) = x - 3
Problem 2 :
f(x) = x – 3
g(x) = 4x + 8
Problem 3 :
f(x) = log_{10}(x)
g(x) = 10^{x}
Problem 4 :
f(x) = x – 3
g(x) = -5x
Problem 5 :
f(x) = x
g(x) = 3x + 8
1. Answer :
f(x) = x + 3
g(x) = x - 3
To check whether f(x) and g(x) are inverse to each other, find f o g and g o f.
f o g :
f o g = f[g(x)]
= f[x + 3]
= x + 3 - 3
= x ----(1)
g o f :
g o f = g[f(x)]
= g[x - 3]
= x - 3 + 3
= x ----(2)
From (1) and (2),
f o g = g o f = x
So, f(x) and g(x) are inverse to each other.
2. Answer :
f(x) = x – 3
g(x) = 4x + 8
f o g :
f o g = f[g(x)]
= f[4x + 8]
= 4x + 8 - 3
= 4x + 5 ≠ x
Because f o g ≠ x, we don't have to find g o f. And f(x) and g(x) are not inverse to each other.
3. Answer :
f(x) = log_{10}(x)
g(x) = 10^{x}
f o g :
f o g = f[g(x)]
= f[10^{x}]
= log_{10}(10^{x})
= xlog_{10}10
= x(1)
= x ----(1)
g o f :
g o f = g[f(x)]
= g[log_{10}(x)]
= 10^{log10(x)}
= x ----(2)
From (1) and (2),
f o g = g o f = x
So, f(x) and g(x) are inverse to each other.
4. Answer :
f(x) = x – 3
g(x) = -5x
f o g :
f o g = f[g(x)]
= f [-5x]
= -5x - 3 ≠ x
Because f o g ≠ x, we don't have to find g o f. And f(x) and g(x) are not inverse to each other.
5. Answer :
f(x) = x
g(x) = 3x + 8
f o g :
f o g = f[g(x)]
= f[3x + 8]
= 3x + 8 ≠ x
Because f o g ≠ x, we don't have to find g o f. And f(x) and g(x) are not inverse to each other.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Jan 17, 22 10:45 AM
Trigonometry Word Problems Worksheet with Answers
Jan 17, 22 10:41 AM
Trigonometry Word Problems with Solutions
Jan 16, 22 11:56 PM
Writing Numbers in Words Worksheet