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if f(x) = 1/(1-x) and g(x) = (x-1)/ x then gof (x) is
- a)x-1
- b)x
- c)1/x
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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if f(x) = 1/(1-x) and g(x) = (x-1)/ x then gof (x) isa)x-1b)xc)1/xd)No...
To find the composition of two functions, we substitute the expression of one function into the other function. In this case, we are given f(x) = 1/(1-x) and g(x) = (x-1)/x, and we need to find g o f(x).
To find g o f(x), we substitute f(x) into g(x):
g o f(x) = g(f(x))
Replacing f(x) in g(x), we get:
g o f(x) = g(1/(1-x))
Let's simplify this expression step by step:
First, let's find the value of g(1/(1-x)):
g(1/(1-x)) = ((1/(1-x)) - 1) / (1/(1-x))
Now, let's simplify the numerator:
((1/(1-x)) - 1) = (1 - (1-x)) / (1-x)
= (1 - 1 + x) / (1-x)
= x / (1-x)
Now, let's substitute this back into the expression for g o f(x):
g o f(x) = (x / (1-x)) / (1/(1-x))
Now, let's simplify the division of fractions:
g o f(x) = (x / (1-x)) * ((1-x) / 1)
= x / 1
= x
Therefore, g o f(x) simplifies to x. Hence, the correct answer is option B: x.
In summary, to find the composition of two functions, we substitute the expression of one function into the other function. In this case, we substituted f(x) = 1/(1-x) into g(x) = (x-1)/x to find g o f(x), which simplifies to x.
To find g o f(x), we substitute f(x) into g(x):
g o f(x) = g(f(x))
Replacing f(x) in g(x), we get:
g o f(x) = g(1/(1-x))
Let's simplify this expression step by step:
First, let's find the value of g(1/(1-x)):
g(1/(1-x)) = ((1/(1-x)) - 1) / (1/(1-x))
Now, let's simplify the numerator:
((1/(1-x)) - 1) = (1 - (1-x)) / (1-x)
= (1 - 1 + x) / (1-x)
= x / (1-x)
Now, let's substitute this back into the expression for g o f(x):
g o f(x) = (x / (1-x)) / (1/(1-x))
Now, let's simplify the division of fractions:
g o f(x) = (x / (1-x)) * ((1-x) / 1)
= x / 1
= x
Therefore, g o f(x) simplifies to x. Hence, the correct answer is option B: x.
In summary, to find the composition of two functions, we substitute the expression of one function into the other function. In this case, we substituted f(x) = 1/(1-x) into g(x) = (x-1)/x to find g o f(x), which simplifies to x.
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if f(x) = 1/(1-x) and g(x) = (x-1)/ x then gof (x) isa)x-1b)xc)1/xd)None of theseCorrect answer is option 'B'. Can you explain this answer?
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