contestada

Let h(x)=2x+5h(x)=2x+5h, left parenthesis, x, right parenthesis, equals, 2, x, plus, 5 and g(x)=8-3xg(x)=8−3xg, left parenthesis, x, right parenthesis, equals, 8, minus, 3, x. What is the value of h(g(1.5))h(g(1.5))h, left parenthesis, g, left parenthesis, 1, point, 5, right parenthesis, right parenthesis?

Respuesta :

silvio
8x equal 5 - six because is a parenthesis
kudzordzifrancis

The given functions were

[tex]h(x)=2x+5\: and\:g(x)=8-3x[/tex]


Before we can evaluate [tex]h(g(1.5))[/tex] we need to find an expression for  [tex]h(g(x))[/tex].

This is the composition of the two functions. [tex]h(g(x))[/tex] means [tex]g(x)[/tex] becomes an input for [tex]h(x)[/tex]. This means that;

[tex]h(g(x))=h(8-3x)[/tex]

So we need to substitute, [tex]8-3x[/tex] wherever we see [tex]x[/tex] in [tex]h(x)[/tex]

[tex]\Rightarrow h(g(x))=2(8-3x)+5[/tex]

We expand the bracket to obtain;

[tex]h(g(x))=2\times8-2\times3x+5[/tex]

Simplify to obtain;

[tex]h(g(x))=16-6x+5[/tex]

[tex]h(g(x))=21-6x[/tex]

Now we substittute [tex]x=1.5[/tex] in to [tex]h(g(x))=21-6x[/tex] to obtain,

[tex]\Rightarrow h(g(1.5))=21-6(1.5)[/tex]

[tex]\Rightarrow h(g(1.5))=21-9[/tex]

[tex]\Rightarrow h(g(1.5))=12[/tex]

Hence, the value of [tex]h(g(1.5))[/tex] is [tex]1.5[/tex].




Otras preguntas