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TK
Lv 4
TK asked in Science & MathematicsMathematics · 1 decade ago

Solving a function g(x)?

h(x) = 2+5x

gh(x) = x/2 + 1

g(x) = ?

Thanks

Update:

If you have more than 1 way, please write out both ways please, thanks.

Update 2:

h(x) = 2+5x

gh(x) = (x/2) + 1

g(x) = ?

GeniusAyaz got it right, but how u did it?

4 Answers

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  • Como
    Lv 7
    1 decade ago
    Favorite Answer

    g (2 + 5x) = x/2 + 1

    Let y = 2 + 5x

    5x = y - 2

    x = (1/5) y - 2/5

    g (y) = (1/2) [ (1/5) y - 2/5 ] + 1

    g ( y ) = (1/10) y + 4/5

    g ( x ) = (1/10) x + 4/5

  • Hemant
    Lv 7
    1 decade ago

    H(x) = 2 +5x and ( G o H ) = ( x/2 ) + 1.

    G[ H(x) ] = (x/2) + 1

    G ( 2 + 5x ) = ( x/2 ) + 1...............( 1 )

    Now, let 2 + 5x = k.

    Then, 5x = k - 2, x = ( k - 2 )/5.

    Hence, from ( 1 ),

    G ( k ) = ( 1/2 )( k - 2 )/5 + 1 =( k - 2 )/10 + 1 = ( k+ 8 )/ 10.

    Replacing k by x, G (x ) = ( x + 8 ) / 10..............................Ans.

  • Retsum
    Lv 6
    1 decade ago

    Since h(x) and g(h(x)) are linear functions, g(x) must be linear.

    Let g(x) = ax + b

    g(h(x)) = a(2 + 5x) + b = 5ax + 2a + b = (x/2) + 1

    Compare coefficients

    5a = 1/2

    a = 1/10

    2a + b = 1

    1/5 + b = 1

    b = 4/5

    g(x) = (1/10)x + 4/5

  • Anonymous
    1 decade ago

    g(x)= x/10 + 4/5

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