If f(x) = x2 - 4x + 3, then find the values of (a) f(1) (b) f(-1) (c) f(2) (d) f(3)
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If f(x) = x2 - 4x + 3, then find the values of (a) f(1) (b) f(-1) (c) f(2) (d) f(3)
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Step-by-step explanation:
[tex]\green{\bold{\underline{ ✪ UPSC-ASPIRANT✪ }}}[/tex]
[tex]\red{\bold{\underline{\underline{QUESTION:-}}}}[/tex]
Q:-solve and verify the equation
[tex] \frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{ 3} )[/tex]
[tex]\huge\tt\underline\blue{Answer }[/tex]
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[tex]⟹
\frac{1}{3} x - 4 = x - ( \frac{1}{2} + \frac{x}{3} )[/tex]
[tex]⟹
\frac{x}{3} - 4 = x - ( \frac{3 + 2x}{6} )[/tex]
[tex]⟹
\frac{x - 12}{3} = x - ( \frac{2x + 3}{6} )[/tex]
[tex]⟹
\frac{x - 12}{3} = x - \frac{2x - 3}{6} [/tex]
[tex]⟹
\frac{x - 12}{3} = \frac{6x - 2x - 3}{6} [/tex]
[tex]⟹
\frac{x - 12}{3} = \frac{4x - 3}{6} [/tex]
cancelling 6( R.H.S) By 3 From L.H.S
[tex]⟹ \frac{x - 12}{1} = \frac{4x - 3}{2}
[/tex]
[tex]⟹
2(x - 12) = 4x - 3[/tex]
[tex]⟹
2x - 24 = 4x - 3[/tex]
[tex]⟹
- 24 + 3 = 4x - 2x[/tex]
[tex]⟹
- 21 = 2x[/tex]
[tex]⟹
x = - \frac{21}{2} [/tex]
CHECK:-
[tex]⟹ \frac{ - \frac{21}{2} }{3} - 4 = - \frac{21}{2} - ( \frac{1}{2} + ( - ) \frac{ \frac{21}{2} }{3} )
[/tex]
[tex]⟹
- \frac{21}{6} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{21}{6} )[/tex]
[tex]⟹
- \frac{7}{2} - 4 = - \frac{21}{2} - ( \frac{1}{2} - \frac{7}{2} )[/tex]
[tex]⟹
\frac{ - 7 - 8}{2} = - \frac{21}{2} - ( - \frac{6}{2} )[/tex]
[tex]⟹ - \frac{15}{2} = - \frac{21}{2} - ( - 3)
[/tex]
[tex]⟹
- \frac{15}{2} = - \frac{21}{2} + 3[/tex]
[tex]⟹
- \frac{15}{2} = \frac{ - 21 + 6}{2} = - \frac{15}{2} [/tex]
THEREFORE,L.H.S=R.H.S
VERIFIED✔️
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HOPE IT HELPS YOU..
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Thankyou:)