If the domain of the function f(x) = x2
-6x +7 (-ALPA,ALPA) then the range of function is
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Answer:
Let y=x
2
−6x+7
⇒x
2
−6x+7−y=0
On comparing with ax
2
+bx+c=0, we get
a=1, b=−6 and c=(7−y)
Now,
x=
a
−b±
b
2
−4ac
=
2
6±
36−4(7−y)
=
2
6±
36−28+4y
=
2
6±
4y+8
=
2
6±2
y+2
=3±
y+2
f(x) is defined only when
y+2≥0⇒y≥−2
∴ Range of f(x)=[−2,∞).
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