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08 Feb 2022, 03:30
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If \(f(x) = x^2 + 1\) and \(g(x) = x^2 – 1\), what is the value of \(g(f(x))\)?
A. \(x^2\)
B. \(x^4 – 1\)
C. \(x^4 + 2x^2\)
D. \(x^2 + 2x\)
E. \(x^4 + 2x^2 + 2\)
A. \(x^2\)
B. \(x^4 – 1\)
C. \(x^4 + 2x^2\)
D. \(x^2 + 2x\)
E. \(x^4 + 2x^2 + 2\)
08 Feb 2022, 03:46
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Bunuel
If \(f(x) = x^2 + 1\) and \(g(x) = x^2 – 1\), what is the value of \(g(f(x))\)?
A. \(x^2\)
B. \(x^4 – 1\)
C. \(x^4 + 2x^2\)
D. \(x^2 + 2x\)
E. \(x^4 + 2x^2 + 2\)
A. \(x^2\)
B. \(x^4 – 1\)
C. \(x^4 + 2x^2\)
D. \(x^2 + 2x\)
E. \(x^4 + 2x^2 + 2\)
we know that \(f(x) = x^2 + 1\) and \(g(x) = x^2 – 1\)
Substitute the value of f(x) for x in g(x)
\(g(f(x))\) = \((x^2+1)^2 – 1\) =\((x^2)^2+1 + 2x^2 -1\) =\( x^4 + 2x^2\) -> option C
21 Aug 2022, 11:37
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Given that \(f(x) = x^2 + 1\) and \(g(x) = x^2 – 1\) and we need to find the value of g(f(x))
To find g(f(x)) lets first substitute the value of f(x) we get
g(f(x)) = g(\(x^2 + 1\))
Now, to find the value of g(\(x^2 + 1\)) we need to compare what is inside the bracket () in g(\(x^2 + 1\)) and g(x)
=> We need to substitute x with \(x^2 + 1\) in \(g(x) = x^2 – 1\) to get the value of g(\(x^2 + 1\))
=> \(g(x^2 + 1) = (x^2 + 1)^2 – 1\) = \(x^4 + 2*x^2*1 + 1^1 - 1\) = \(x^4 + 2x^2\)
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
To find g(f(x)) lets first substitute the value of f(x) we get
g(f(x)) = g(\(x^2 + 1\))
Now, to find the value of g(\(x^2 + 1\)) we need to compare what is inside the bracket () in g(\(x^2 + 1\)) and g(x)
=> We need to substitute x with \(x^2 + 1\) in \(g(x) = x^2 – 1\) to get the value of g(\(x^2 + 1\))
=> \(g(x^2 + 1) = (x^2 + 1)^2 – 1\) = \(x^4 + 2*x^2*1 + 1^1 - 1\) = \(x^4 + 2x^2\)
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
