TO 2. (2-a) | 3. If f:R+ → (8,00) defined by f(x)= x² +8, then find f-'(x).
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Answered by
1
Answer:
f:R
1
→(4,∞)
f(x)=x
2
+4
f(x
1
)=f(x
2
)
x
1
2
+4=x
2
2
+4
x
1
=x
2
f(x) is on-one.
f(x)=x
2
+4
y=x
2
+4
x
2
=y−4
x=
y−4
f(x)=x
2
+4
f(x)=(
y−4
)
2
+4
f(x)=y−4+4
f(x)=y
f(x) is onto function.
So,f(x) is bijective, Hence it is invertible
f(x)=x
2
+4
y=x
2
+4
y=x
2
−4
y=
x
2
−4
f
−1
(x)=
x−4
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Answer:
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